The Space Between Algorithms: Grading Degrees of Freedom

Abstract

A sorting routine has no freedom; it does exactly one thing. A human has a great deal. In between lies a vast space: fixed neural networks, learning agents, a living cell. This playground proposes a way to place any algorithmic system on that spectrum, a composite "freedom score" built from five indicators. The score is an exact weighted blend, which the calibration pins, while being honest that "freedom" here is a constructed measure, not a claim about free will.

Freedom as an index

There is no agreed scalar for how free a system is. So the playground does what fields from development economics to well-being research do with similarly fuzzy concepts: it builds a composite indicator. Five normalized quantities, each in [0, 1], are blended into a single 0-to-100 score:

  • Intra-choice entropy (weight 0.25): how much genuine variety is in the system's choices.
  • Empowerment (0.25): an information-theoretic measure of how much the system's actions shape its own future.
  • Policy-manifold volume (0.2): the size of the space of behaviours it can adopt.
  • Causal emergence (0.2): how much higher-level causal structure arises above the micro-dynamics.
  • Descriptive regularity (0.1): how compressible, hence law-like, its behaviour is.

The exact part

The blending is a convex combination: the five weights sum to exactly one, so the score is a true weighted average, then scaled by 100. That makes a few things exactly checkable, and the calibration verifies each: all indicators at zero give 0, all at one give 100, the weights sum to 1, and turning on only the two 0.25-weighted components yields exactly 50. The arithmetic is the solid floor under the interpretation.

Where the concepts come from

The indicators are inspired by real theory: empowerment is a genuine information-theoretic notion of agency (Klyubin and colleagues), causal emergence draws on Hoel's work on when macro-scales carry more causal weight than micro. But the specific normalizations, the choice of five indicators, and the weights are modelling decisions, not consequences of those theories. A different analyst could pick different components or weights and rank the same systems differently. The assumptions panel is explicit about this.

What the presets claim

The presets place example systems, a sorting algorithm near zero, a fixed neural net low, a learning agent higher, a cell higher still, a human near the top, at illustrative points on the indicators. These are hand-chosen intuitions to give the score surface some anchors, not measurements. Estimating these indicators for a real running system is a hard, separate problem the playground does not attempt; it lets you set the indicators directly and explore the resulting score.

What it is

A conceptual instrument for thinking about gradations of autonomy, the space between rigid and free, with an exact, transparent scoring rule underneath. It is not a benchmark, and a high score is not a claim that a system is conscious or genuinely free. The math is exact; the meaning is a lens.

References

  • Klyubin, A. S., Polani, D., and Nehaniv, C. L. (2005). Empowerment: a universal agent-centric measure of control.
  • Hoel, E. P. (2017). When the map is better than the territory. (Causal emergence.)
  • Standard references on composite-indicator construction.